Constructible Sets in Real Geometry

This book presents a systematic and unified report on the minimal description of constructible sets. It starts at a very basic level (almost undergraduate) and leads up to state-of-the-art results, many of which are published in book form for the very first time. The book contains numerous examples, 63 figures and each chapter ends with a section containing historical notes. The authors tried to keep the presentation as self-contained as it can possibly be. TOC:Contents: A First Look at Semialgebraic Geometry.- Real Algebra.- Spaces of Signs.- Spaces of Orderings.- The Main Results.- Spaces of Signs of Rings.- Real Algebra of Excellent Rings.- Real Analytic Geometry.